Stability of a nonlinear Volterra integro-differential equation via a fixed point approach

Volume 9, Issue 1, pp 200--207 http://dx.doi.org/10.22436/jnsa.009.01.18

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Authors

Sebaheddin Şevgin - Faculty of Sciences, Department of Mathematics, Yuzuncu Yil University, 65080 Van, Turkey. Hamdullah Şevli - Department of Mathematics, Faculty of Sciences and Arts, Istanbul Commerce University, 34672 Uskudar, Istanbul, Turkey.

Abstract

The object of the present paper is to examine the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of a nonlinear Volterra integro-differential equation by using the fixed point method.

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Keywords

• Hyers-Ulam stability
• Hyers-Ulam-Rassias stability
• Volterra integro-differential equations
• fixed-point method.

MSC

•  45J05
•  47H10
•  45M10

References

• [1] M. Akkouchi, Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a fixed point approach , Acta Univ. Apulensis Math. Inform., 26 (2011), 257-266.
  • MathSciNet
  • Google Scholar
  • MATH


• [2] L.Cădariu, V. Radu , On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber., 346 (2004), 43-52.
  • MathSciNet
  • Google Scholar


• [3] L. P. Castro, A. Ramos , Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 3 (2009), 36-43.
  • View Article
  • MathSciNet
  • Google Scholar


• [4] L. P. Castro, A. Ramos, Hyers-Ulam and Hyers-Ulam-Rassias stability of Volterra integral equations with delay, Integral methods in science and engineering, Birkhauser Boston, Inc., Boston, MA, 1 (2010), 85-94.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] J. B. Diaz, B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] M. Gachpazan, O. Baghani , Hyers-Ulam stability of Volterra integral equation, J. Nonlinear Anal. Appl., 1 (2010), 19-25.
  • Google Scholar


• [7] M. Gachpazan, O. Baghani , Hyers-Ulam stability of nonlinear integral equation, Fixed Point Theory Appl., 2010 (2010), 6 pages.
  • View Article
  • Google Scholar


• [8] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222-224.
  • View Article
  • Google Scholar


• [9] S. M. Jung, A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl., 2007 (2007), 9 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [10] S. M. Jung , A fixed point approach to the stability of differential equations \(y' = F(x; y)\), Bull. Malays. Math. Sci. Soc., 33 (2010), 47-56.
  • MathSciNet
  • Google Scholar
  • MATH


• [11] S.M. Jung, S. Şevgin, H. Şevli, On the perturbation of Volterra integro-differential equations, Appl. Math. Lett., 26 (2013), 665-669.
  • View Article
  • MathSciNet
  • Google Scholar


• [12] J. R. Morales, E. M. Rojas, Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay, Int. J. Nonlinear Anal. Appl., 2 (2011), 1-6.
  • Google Scholar
  • MATH


• [13] T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.
  • View Article
  • MathSciNet
  • Google Scholar


• [14] S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, Inc., New York (1964)
  • Google Scholar